Blow-Up Ratio and Blown Film Gauge

A blown-film bubble is a mass balance you can stand and watch. Melt leaves an annular die through a gap $h_d$ at a diameter $D_d$, air trapped inside inflates it to a bubble of diameter $D_b$, and the nip rolls at the top of the tower pull it away faster than it left the die. Two stretches, one in each direction, and whatever they multiply to, the film thickness divides by.

The blow-up ratio is $D_b/D_d$ — how much wider the bubble is than the die. The draw-down ratio is the nip speed divided by the speed the melt leaves the die lips. Since the volume flowing through any horizontal section is the same, the gauge comes out as $t = h_d/(\mathrm{BUR}\cdot\mathrm{DDR})$. Nothing else is needed, provided you remember that the die gap, not the die diameter, is the thickness the film starts from.

In practice nobody measures the bubble diameter directly — you cannot get a caliper round a moving bubble two storeys up. What is measured is the lay-flat width after the collapsing frame, which is half the bubble's circumference: $W = \pi D_b/2$. Work the diameter back out of that when you need it, and be careful not to feed a lay-flat straight into an equation expecting a diameter — the two differ by $\pi/2$, which is 57 % and produces perfectly believable nonsense.

The two stretches do different things to the film, and that is the craft of the process. Blowing the bubble orients the molecules around it — the transverse direction. Drawing it up orients them along the machine direction. A film blown at 2.5:1 with a modest draw comes out reasonably balanced and tears about equally either way. A film run at 1.5:1 with a hard draw is strongly machine-direction oriented: it splits down its length like a bamboo blind. That is a defect in a carrier bag and exactly the point if you are making tape. Common practice for general packaging film sits between about 2:1 and 4:1, and the reason for both bounds is mechanical rather than arithmetic — below about 1.5:1 the film splits, and above about 4:1 the bubble gets unstable, wandering and breathing while the frost line moves and takes the gauge profile with it.

Two things the arithmetic quietly assumes. First, that density does not change between the die and the frost line. It does — melt is roughly 10 to 15 % less dense than the solid film it becomes — so the ratios here are sound but a mass-throughput calculation built on them needs the solid density, not the melt density. Second, that the gauge is uniform round the bubble. It is not: die-gap variation, cooling-air variation and bubble wander all print as a thickness profile, which is why film lines rotate the die or the haul-off — spreading a repeating thick band round the roll instead of building it into a hard ridge that makes the reel unusable.

Finally, note which knobs an operator actually has. Draw-down moves directly with haul-off speed and is easy. Blow-up moves only by adding or removing internal bubble air, which is slower and interacts with the frost-line height and the cooling. Because the gauge depends on the product of the two, the same thickness can be reached many ways — and those ways are not equivalent, because they leave the film with completely different orientation and therefore different tear, impact and shrink behaviour.